Rotation problem with Action Constraint
In the Dopesheet, you need to check the action you're using in this Action constraint for the UpperArm bone, it is called DrumHit.

As you can see its first rotation keyframe is NOT set to W/X/Y/Z values of 1/0/0/0, but 0.721/-0.654/etc, that's why as soon as you enable the constraint it jumps to this angle.

So what you need to do is to change this first frame rotation setting to 1/0/0/0.

Also I don't know why your Snare, which is supposed to be the controller bone (Target), had a driver, so I deleted it for my test, otherwise it couldn't move.

Now when you rotate it on the X axis, it works.